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Quantum Mechanical of Scattering Cross-Section Theory
Published in Maged Marghany, Automatic Detection Algorithms of Oil Spill in Radar Images, 2019
Therefore, long after scattering, which signifies photons distributing in all directions from the scattering center. In this view, the flux of photons is denoted by a spherical wave. On the contrary, Equation 4.5 denotes the flux of photons which corresponds to plane waves (Fig. 4.3). Conversely, a plane wave is characterized by a definite linear momentum ℏk→, but no definite angular momentum. In fact, a plane wave, being in principle, of infinite extension, corresponds to impact parameters varying from zero to infinity. Correspondingly, the angular momenta contained in a plane wave (x, y) also vary from zero to infinity. In this regard, it is possible, therefore, to analyze a plane wave into an infinite number of components each of which corresponds to a definite angular momentum. Each of such components is well known as a partial wave, and the process of decomposing a plane wave into the partial waves is called a partial wave analysis [52–58]. In this view, e(ik→.r→) is considered as a solution of the free-particle Schrödinger equation which defines the linear momentum representing the system as: () H^Ψ(r→)=EΨ(r→)
Scattering of e± from N2 in the energy range 1 eV–10 keV
Published in Molecular Physics, 2020
Mahmudul H. Khandker, Nazifa T. Arony, A. K. F. Haque, M. Maaza, M. Masum Billah, M. Alfaz Uddin
The spin-polarisation during the scattering of electron and positron requires the inclusion of spin-orbit interaction term in the Schrödinger equation. On the other hand, this term is simply incorporated in Dirac's relativistic equation. McEacharan and Stauffer [7] carried out relativistic calculations on the momentum transfer cross section, scattering length and differential cross sections at low energies for the electron-argon scattering. The results produced an excellent agreement with experiments and showed an improvement over the non-relativistic analysis. Encouraged by the above facts, we adopt Dirac partial wave analysis, with complex atomic OPM, to calculate differential cross section (DCS), integrated elastic cross section (IECS), momentum transfer cross section (MTCS), viscosity cross section (VCS), inelastic cross section (INCS), total cross section (TCS) and total ionisation cross section (TICS) for the scattering of electron and positron from nitrogen atom. Then sums of these cross sections of the individual atoms are taken to produce corresponding molecular cross sections. These cross sections obtained in this simplistic way of AR are used for modelling codes for various applications as stated above.
Relativistic treatment of scattering of electrons and positrons by mercury atoms
Published in Molecular Physics, 2019
M. M. Haque, A. K. F. Haque, Prajna P. Bhattacharjee, M. Alfaz Uddin, M. Atiqur R. Patoary, A. K. Basak, M. Maaza, B. C. Saha
In the literature, there are widespread theoretical studies on the projectile–atom scattering employing OP model (OPM). The present work reports the scattering of electron and positron from mercury atoms embodying a complex OPM within the framework of Dirac relativistic partial wave analysis (DRPWA). After generating the full OP for the above scattering systems, the Dirac equation is solved numerically to calculate the scattering characteristics. The imaginary part of our OP represents the absorption potential that takes into account the loss of particle flux to all energetically possible inelastic channels. The real part of OP comprises the static, exchange and polarisation potentials. In our previous calculations of -atom scattering [43–45], we used a global polarisation potential that was a combination of the long-range Buckingham polarisation potential and a short-range local density approximation (LDA) correlation potential. In the present study, the Buckingham polarisation potential is replaced by a parameter-free polarisation potential of Sun et al. [46]. Its inclusion yields better results over a wide energy range (1.0 eV 10.0 keV). Very recently, we have successfully used the same polarisation potential but with absorption potential of adjustable strength for the calculation of spin polarisation and spin polarisation parameters of elastic -Hg scattering [47]. The present DRPWA results of DCS, IECS, MTCS, VCS, INECS and TCS, generated from the direct and spin-flip scattering amplitudes and , respectively, are compared with the available experimental data [6–9,14,15,48–50] and other calculations [16,17,20,21,23,24,36].
Theoretical study of e ±-NH3 scattering
Published in Molecular Physics, 2022
Nira Akter, M. Nure Alam Abdullah, M. Shorifuddoza, M. Atiqur R. Patoary, M. Masum Billah, Mahmudul H. Khandker, M. Maaza, Hiroshi Watabe, A. K. F. Haque, M Alfaz Uddin
Figures 3–7 display the angular DCSs for -NH3 scattering calculated using the IAM and IAMS methods at impact energies 7.5 eV–1 MeV, and compared with the available experimental measurements [8,35,37–39] and theoretical calculations [38,43,49,53,54,76,77]. In Figure 3(a)–(f), DCSs at energies 7.5–40 eV, calculated using the IAM and IAMS, show a disagreement in magnitudes with experimental [8] and theoretical [38,49,53,54] works but agree in number and position of minima in most of the cases. At 7.5 eV incident energy, depicted in Figure 3(a), the IAM method overestimates the cross sections throughout the whole angular range, while the calculated DCSs using the IAMS method agree both in magnitude and pattern with the works [8,38,49] in the backward angles . At this energy point, the calculations of Homem et al. [38] using a single-centre-expansion technique together with Padé's method [78] and R-matrix calculations of Munjal and Baluja [49] show a good agreement with the experimental data [8]. These differences are not unexpected. Munjal and Baluja [49] have used the R-matrix dynamics, more sophisticated method than Dirac's partial wave analysis (DPWA), to explain the scattering phenomena at low energies. Moreover, the R-matrix method is applied using the molecular wave function while our method has considered the independent atom model. For 15, 20 and 30 eV projectile energies, as shown in Figure 3(c)–(e), both IAM and IAMS approaches produce the minima at almost the same positions as those produced by other experimental and theoretical works [8,38,49,53,54]. At these three incident energies, the predictions of Mahato et al. [54], Homem et al. [38] (for 15 and 30 eV) and Munjal and Baluja [49] (for 15 and 20 eV) well agree with the experimental DCSs [8]. Although the calculations of Kaur et al. [53] produce good agreement at 20 eV, but underestimate the cross sections at 30 eV throughout the whole angular range. For 30 eV, the calculated DCSs using IAMS agree with the experimental data [8] with an underestimation at minima positions in which the IAM result is in good agreement. There is no experimental data found at 10 eV and a complete disagreement is found between our calculations and those of Kaur et al. [53] and Mahato et al. [54] as observed in Figure 3(b). Our DCS results for IAM and IAMS methods show unusual pattern and disagree with the experimental data at energies eV. This may be due to ignoring the multiple scattering of electrons from the constituent atoms of the NH3 target and internal structure of the molecule. At low energies, de Broglie wavelengths of the projectile are comparable to the size of the target molecule and as such the projectile can ‘see’ the internal structure of the target. So the IAM and IAMS cannot predict the aforesaid scattering from the molecular target.